Phase transitions in soft-committee machines

Equilibrium statistical physics is applied to the off-line training of
layered neural networks with differentiable activation functions.
A first analysis of soft-committee machines with an arbitrary number
(K) of hidden units and continuous weights learning a perfectly matching rule is performed.
Our results are exact in the limit of high training temperatures .
For K=2 we find a second-order phase transition from unspecialized to
specialized student configurations at a critical size P of the training set,
whereas for the transition is first order.
The limit can be performed analytically, the transition occurs after presenting
on the order of examples. However, an unspecialized metastable state
persists up to .

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